The Post Office’s Historical Shortfall Scheme was launched in May for present and former postmasters who experienced shortfalls as a result of failures of the Horizon computer database.
The scheme was launched a month after 39 former post office staff were granted appeals against convictions for fraud or false accounting.
Rubbina Shaheen, who kept a post office in Shrewsbury and Tracy Felstead, who lives in Telford, are among those fighting to clear their names after being jailed for discrepancies they say were caused by computer errors.
Last year the Post Office agreed to a £57.75 million out-of-court settlement with 555 ex-post office staff – including Miss Felstead – following a group action in the High Court.
The closing date for applications is August 14. Nick Read, group chief executive of the Post Office, said bosses were keen to make amends for where the group had “got things wrong”.
He said: “This scheme is an important milestone that demonstrates a more open and transparent relationship with postmasters and offers redress for those who may have experienced shortfalls related to previous versions of the computer system Horizon.”
Bosses at the Post Office said the computer glitches related to previous versions of the Horizon system, and sought to reassure workers and customers the version in use today was reliable.
Mrs Shaheen, 54, who kept Greenfields Post Office in Shrewsbury, was jailed for 12 months in 2010 for false accounting. Miss Felstead, 37, of Brookside, Telford, was jailed for six months in 2001 accused of stealing £11,500 while working as an 18-year-old counter clerk.
They were granted appeals following a ruling by High Court judge Mr Justice Fraser that the Horizon system could have led to people being wrongly accused.
Last month, the BBC Panorama programme claimed the Post Office was aware its system could have been to blame for the shortfall as it pressed ahead with the prosecutions.
For details on the scheme see onepostoffice.co.uk/scheme